It can be anywhere from a few weeks to a few months but do chase them up if they've given you timelines that they haven't stuck to or if you haven't heard anything for more than 4 weeks at a time. Not everywhere will tell you if you've been rejected.

I had an e-mail from Edinburgh a week ago saying they'd get back to me in 4-6 weeks and I heard back yesterday, seems remarkably quick! For my application to St Andrews, I heard in early February, having submitted my application mid-January. Hope that helps!

can be both ways but most send you an email informing you that they received your application. Universities at london have a very high amount of applicants and therefore usually take longer to reply. for king's i waited liked 6 weeks for my reply while from universities that are not located in London it took like 2 weeks. If the university takes longer time than its stated in their website to reply maybe you can send them an email to verify that they received your application.